Point-by-point measurements of relative optical path length displacements can be made over a range of such optical displacements by measuring rates of interferometric phase variation with wavenumber. For example, a spatially coherent source beam composed of multiple wavelengths, i.e., a low temporally coherent beam, or a succession of different wavelengths can be divided by a beamsplitter into an object beam that is reflected from the test object and a reference beam that is reflected from a reference reflector. Reflected light from both the test object and the reference reflector is recombined at a beamsplitter into a measurement beam and refocused within a detector such as a spectrometer, which records interference intensities of the different spectral components of the returning measurement beam. Based on the relationship between (a) the rate of change in interference phase with the change in beam frequency, referred to a modulation frequency, and (b) the optical path length difference between the object and reference beams, the relative optical displacements between different measured points can be ascertained.
The interferometric components that divide the source beam into object and reference beams and then recombine the object and reference beams into a common measurement beam can be contained within an optical pen that also directs the object beam to and from a test object. Assembling the interferometric components together within the optical pen can diminish the possibility of unwanted disturbances having differential effects on the object and reference beams, which can reduce measurement accuracy and reliability.
However, the number and complexity of components required to house an interferometer within an optical pen can add bulk and complexity to the optical pen, which must be relatively movable with respect to a test object to acquire a range of measurement points on the test object. Particularly in instances where the optical path lengths of the object and reference beams traversing respective object and reference arms of the interferometer are required to be of comparable length, the two arms of the interferometer can add to the size and distort the shape of the optical pen in ways that can interfere with the required relative movement of the optical pen over test objects having various surface shapes. For example, while the object arm can be aligned with a central axis of the optical pen, the reference arm is generally offset from the central axis, which both increases the size and distorts the shape of the optical pen from axial symmetry. Interferometric arrangements such as Mirau interferometers can significantly reduce the working distance between the optical pen and test objects.